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6 answers

Quasicrystals and the Riemann Hypothesis

Let $0 < k_1 < k_2 < k_3 < \cdots $ be all the zeros of the Riemann zeta function on the critical line: $$ \zeta(\frac{1}{2} + i k_j) = 0 $$ Let $f$ be the Fourier transform of the sum of Dirac deltas supported at these points. In other words: $$…
John Baez
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94
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7 answers

When does Cantor-Bernstein hold?

The Cantor-Bernstein theorem in the category of sets (A injects in B, B injects in A => A, B equivalent) holds in other categories such as vector spaces, compact metric spaces, Noetherian topological spaces of finite dimension, and well-ordered…
Randomblue
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93
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9 answers

Is Mac Lane still the best place to learn category theory?

For a student embarking on a study of algebraic topology, requiring a knowledge of basic category theory, with a long-term view toward higher/stable/derived category theory, ... Is Mac Lane still the best place to start? Or has the day arrived…
cdouglas
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93
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5 answers

Note rejected from arXiv: what to do next?

Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no feedback as to why and does not answer questions. I…
Gro-Tsen
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20 answers

Short papers for undergraduate course on reading scholarly math

(I know this is perhaps only tangentially related to mathematics research, but I'm hoping it is worthy of consideration as a community wiki question.) Today, I was reminded of the existence of this paper: Terminating Decimals in the Cantor Set. It…
Brendan W. Sullivan
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93
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1 answer

Volumes of sets of constant width in high dimensions

Background The $n$-dimensional Euclidean ball of radius $1/2$ has width $1$ in every direction. Namely, when you consider a pair of parallel tangent hyperplanes in any direction the distance between them is $1$. There are other sets of constant…
Gil Kalai
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93
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5 answers

Can a row of five equilateral triangles tile a big equilateral triangle?

Can rotations and translations of this shape perfectly tile some equilateral triangle? I originally asked this on math.stackexchange where it was well received and we made some good progress. Here's what we learnt: Because the area of the…
Oscar Cunningham
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93
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6 answers

How do I see LaTeX math on any web page and in email?

This is a follow up to this closed question. I open a random page, such as something on arXiv at 8:05 p.m. EST, and I see all these dollar signs, and I sigh and I wish that I could see nicely formatted math formulas instead, just like on MO. Is it…
VA.
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5 answers

Is there a dense subset of the real plane with all pairwise distances rational?

I heard the following two questions recently from Carl Mummert, who encouraged me to spread them around. Part of his motivation for the questions was to give the subject of computable model theory some traction on complete metric spaces, by…
Joel David Hamkins
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92
votes
74 answers

Pseudonyms of famous mathematicians

Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles Lutwidge) Dodgson. Needless to say, L. Carroll was his…
Denis Serre
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92
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2 answers

Will this Turing machine find a proof of its halting?

Consider the following Turing machine $M$: it searches over valid ZFC proofs, in lexicographic order, and if it finds a proof that $M$ halts, then it halts. If we fix a particular model of Turing machine (say single-tape Turing machine), and if we…
Henry Yuen
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92
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14 answers

Time-saving (technology) tricks for writing papers

I have over the years learned some tricks which saves a lot of time, and I wish I had known them earlier. Some tricks are LaTeX-specific, but other tricks are more general. Let me start with a few examples: Use LaTeX macros and definitions for easy…
Per Alexandersson
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92
votes
9 answers

Examples where physical heuristics led to incorrect answers?

I have always been impressed by the number of results conjectured by physicist, based on mathematically non-rigorous reasoning, then (much) later proved correct by mathematicians. A recent example is the $\sqrt{2+\sqrt{2}}$ connective constant of…
Alekk
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92
votes
2 answers

Coming out as transgender in the mathematical community

I don't know if MO is the right place to ask such a question, but anyway it's my only hope to get an answer, and it's very important for me (not to say 'vital'); so let's try. I'm at this time a Ph.D. student, and I plan to defend in the spring of…
Rdmv
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0 answers

Hironaka's proof of resolution of singularities in positive characteristics

Recent publication of Hironaka seems to provoke extended discussions, like Atiyah's proof of almost complex structure of $S^6$ earlier... Unlike Atiyah's paper, Hironaka's paper does not have a historical overview that provides a vague image for…
Henry.L
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